Hexagonal grids offer significant advantages over square or triangular grids due to their compact shape and uniform adjacency. These properties make them especially useful in spatial statistics, modeling, and geospatial analysis.
Compactness
One of the key uses of Discrete Global Grid Systems (DGGS) is spatial aggregation, made effective by consistent cell size and fixed cell locations. Hexagons offer a clear benefit in this context. The distance between adjacent cells remains stable, and orientation does not shift within a local region. When applying point binning to a grid mesh, hexagons minimize the average distance between points and their representative cells. Compared to square grids at the same resolution, they can reduce the number of required cells by approximately 13 percent. Their superior angular resolution also enables better representation of angular relationships among data points.
In a hexagonal grid, all first-order neighbors are equidistant from the central cell. The resulting neighborhood pattern is more circular than those of square or triangular grids. This layout provides a closer approximation to Cartesian distances, making hexagonal distances a reliable surrogate for Euclidean calculations.
Practical Implications for Spatial Operations
Hexagonal grids simplify neighborhood-based operations by removing ambiguity in defining adjacent cells. There is no need for complex weighting schemes or custom adjacency rules. In hydrological modeling, hexagons reduce artificial barriers like the island effect and provide a better approximation of flow width. In image processing tasks that involve radial symmetry, hexagonal grids have been shown to improve computational efficiency by 25 to 50 percent compared to square grids.
A Natural Design Pattern
Interestingly, the foveal region of the human eye uses a hexagonal pattern for high-resolution visual sampling. This biological example illustrates the efficiency of hexagonal tiling in representing space. Similarly, applying hexagons to Earth’s surface provides a more consistent and accurate sampling framework. Research has also shown that the human brain forms internal maps using hexagonal lattice structures across different spatial scales. Emulating this pattern in geospatial applications brings both biological inspiration and analytical advantages.
Hexagonal grids are more than just aesthetically pleasing. Their compactness, symmetry, and consistency make them a practical and powerful foundation for spatial analysis.